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arXiv:1512.00269 · Physical Review A

Entangled microwaves as a resource for entangling spatially separate solid-state qubits: Superconducting qubits, nitrogen-vacancy centers, and magnetic molecules

Angela Gomez, Ferney J. Rodríguez, Luis Quiroga, Juan José García‐Ripoll

Published Jun 27, 2016• 6 citations
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Abstract

Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two-qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Decoherence thermal effects on the entanglement transfer are also discussed. Our results provide evidence that this entanglement transfer by dissipation is feasible, yielding to a steady-state amount of entanglement in the bipartite quantum system which can be optimized for a wide range of realistic physical systems that include state-of-the-art experiments with nitrogen-vacancy centers in diamond, superconducting qubits, or even magnetic molecules embedded in a crystalline matrix.

DOI
10.1103/physreva.93.062336

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Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two-qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Decoherence thermal effects on the entanglement transfer are also discussed. Our results provide evidence that this entanglement transfer by dissipation is feasible, yielding to a steady-state amount of entanglement in the bipartite quantum system which can be optimized for a wide range of realistic physical systems that include state-of-the-art experiments with nitrogen-vacancy centers in diamond, superconducting qubits, or even magnetic molecules embedded in a crystalline matrix.
Nitrogen-vacancy (NV) defect centers in diamond are strong candidates to generate entangled states in solid-state environments even at room temperature. Quantum correlations in spatially separated NV systems, for distances between NVs ranging from a few nanometers to a few kilometers, have been recently reported. In the present paper, we consider the entanglement transfer from two-mode microwave-squeezed (entangled) photons, which are in resonance with the two lowest NV electron spin states, to initially unentangled NV centers. We first demonstrate that the entanglement transfer process from quantum microwaves to isolated NV electron spins is feasible. We then proceed to extend the previous results to more realistic scenarios where 13C^{13}\mathrm{C}13C nuclear spin baths surrounding each NV are included, quantifying the entanglement transfer efficiency and robustness under the effects of dephasing/dissipation noisy nuclear baths. Finally, we address the issue of assessing the possibility of entanglement transfer from the squeezed microwave light to two remote nuclear spins closely linked to different NV centers.
The search for optimal schemes and dissipative environments that can mediate long-range entanglement between two distant nitrogen-vacancy centers (NVCs) in diamond has been the subject of vigorous efforts over the past decade due to potential applications of such microscopic solid-state qubits in quantum sensing and quantum computing. However, stabilizing entanglement of NVCs into a {\em steady state} poses a significant challenge, typically requiring tuning the environment {\em out of equilibrium}. Here we microscopically and rigorously derive a Lindblad quantum master equation (QME) for a system of two {\em driven-dissipative} NVCs, where the drive is microwave radiation and dissipation is provided by a single magnetic bath that is kept in {\em equilibrium}. The jump operators within the Lindblad QME are expressed in terms of Keldysh Green's functions defined as correlators of dipolar field operators of the bath. This QME makes it possible to predict precise conditions for long-range and steady-state entanglement of two NVCs, while suggesting that a synthetic antiferromagnet could be an {\em optimal} choice for a dissipative environment. By using realistic parameters from available experiments, we estimate steady-state concurrence reaching C≃0.28\mathcal{C}\simeq 0.28C≃0.28 for two NVCs separated by ∼100 nm\sim 100 \: \mathrm{nm}∼100nm.
We propose a scheme to generate entanglement between magnon and superconducting qubit. The macroscopic yttrium–iron–garnet sphere and superconducting qubit are installed in two spatially separated cavities, which are directly driven by a two-mode squeezed-vacuum microwave field. The magnon and cavity 1 are coupled via magnetic dipole interaction and the superconducting qubit and cavity 2 are coupled via electric dipole interaction. We theoretically demonstrate that the magnon–qubit steady-state entanglement can be created by transferring quantum correlations of the two-mode squeezed-vacuum driving field via cavity–magnon and cavity–qubit beam-splitter interactions. The transfer is highly efficient, and the entanglement is robust against temperature in the optimal parameter regimes. We also deduce a new, to the best of our knowledge, mathematical method to analyze the dynamics of the magnon–qubit entanglement and some significant results are obtained. Our scheme can be implemented with experimentally feasible parameters and may provide guidance in designing hybrid quantum networks.
Entanglement properties are studied in the continuous-variable system of three nitrogen-vacancy center ensembles cou-pled to separate transmission line resonators interconnected by current-biased Josephson junction. The circuit is enhanced by Josephson parametric amplifier, which serves as source of squeezed microwave field. Bosonic modes of nitrogen-vacancy-center ensembles exhibit steady state entanglement for certain range of parameters. Squeezed microwave field can be consider as a driving force of entanglement. Proposed scheme provides generating entanglement for each of the three pairs of spin ensembles.
A dissipative scheme is proposed to generate single- or two-mode squeezed states in a hybrid quantum system consisting of superconducting resonators and nitrogen-vacancy-center ensembles (NVEs). For the single-mode squeezing generation, we consider an array of linearly coupled superconducting resonators, each of which is magnetically coupled to a NVE. In addition, one of the resonators is coupled to a gap-tunable qubit. It is shown that at steady state all the resonators and NVEs in the array can enter into single-mode squeezed states via dissipation of the qubit. For the two-mode squeezing realization, we consider a pair of superconducting resonator chains, which are coupled to two gap-tunable qubits. We find that at steady state all the resonator pairs in the up and down chains will be steered into two-mode squeezed states via dissipation of the qubits. The present scheme has a remarkable feature: only one or two gap-tunable dissipative qubits are locally involved, and no squeezing resource is required.
We propose an efficient scheme for transferring quantum states and generating entangled states between two qubits of different nature. The hybrid system consists of a single nitrogen-vacancy (NV) center and a superconducting (SC) qubit, which couple to an optical cavity and a microwave resonator, respectively. Meanwhile, the optical cavity and the microwave resonator are coupled via the electro-optic effect. By adjusting the relative parameters, we can achieve high-fidelity quantum state transfer as well as highly entangled states between the NV center and the SC qubit. This protocol is within the reach of currently available techniques, and may provide interesting applications in quantum communication and computation with single NV centers and SC qubits.